Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE"while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

public class Solution {    public int numDistinct(String S, String T) {        if (S == null || T == null) return 0;        if (T.length() == 0) return 1;        if (S.length() == 0) return 0;                if (S.length() == 1 && T.length() == 1) {            if (S.charAt(0) != T.charAt(0)) {                return 0;            } else {                return 1;            }        }                if (S.charAt(0) != T.charAt(0)) {            return numDistinct(S.substring(1), T);        } else {            return numDistinct(S.substring(1), T.substring(1)) + numDistinct(S.substring(1), T);        }    }}

public class Solution {    public int numDistinct(String S, String T) {        int n = S.length();        int m = T.length();        int[] dp = new int[m];        for (int i = 0; i < n; ++i) {            for (int j = m-1; j >= 0; --j) {                if (T.charAt(j) == S.charAt(i)) {                    if (j==0) dp[0]++;                    else dp[j] += dp[j-1];                }            }        }        return dp[m-1];    }}